The pore geometry of pharmaceutical coatings: statistical modelling, characterization methods and transport prediction
Doctoral thesis, 2020

This thesis contains new methods for bridging the gap between the pore geometry of porous materials and experimentally measured functional properties. The focus has been on diffusive transport in pharmaceutical coatings used in controlled drug delivery systems, but the methods are general and can be applied to other porous materials and functional properties. Relatively large datasets are needed to train realistic models connecting the pore geometry and diffusive transport properties of porous materials. 3-D statistical pore models based on microscopy images of the coating material were in this thesis used to generate large sets of pore structures, in which diffusive transport was computed numerically. Characterization measures capturing important features of the pore geometry were developed and used as predictors of diffusive transport rates in multiplicative regression models. The characterization measures have been implemented in a freely available software, MIST.

In Paper I, a Gaussian random field based pore model was developed and fitted to microscopy images of the coating material. Due to the large size of the data, the model was formulated using a Gaussian Markov random field approximation, which allows for efficient inference. A new method for solving linear equations with Kronecker matrices which reduced the complexity of the model fitting algorithm considerably was developed. The pore model was found to fit the microscopy images well. In Paper II, characterization measures that have been shown to provide good regression models for diffusive transport rates were developed further and implemented. Multiplicative regression models were fitted to pore structures from the model from Paper I, and the new methods were shown to give improved results. In Papers III and V characterization measures that capture a type of bottleneck effect which was observed in another set of microscopy images of the coating material (Papers III and IV), but which is not captured by existing methods, were invented. Pore structures with this type of bottleneck were generated using 3-D statistical pore models, and the new type of bottleneck was found to be an important determinant of diffusive transport rates when the regression models were fitted to simple pore structures (Paper V).

Pascal, Matematiska vetenskaper, Chalmers tvärgata 3
Opponent: Prof. Rasmus Waagepetersen, Department of Mathematical sciences, Aalborg University, Denmark


Sandra Eriksson Barman

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

A three-dimensional statistical model for imaged microstructures of porous polymer films

Journal of Microscopy,; Vol. 269(2018)p. 247-258

Journal article

Barman, S., Fager, C., Röding, M., Lorén, N., von Corswant, C., Olsson, E., Bolin, D., Rootzén, H. New characterization measures of pore shape and connectivity applied to coatings used for controlled drug release

Fager, C., Barman, S., Röding, M., Olsson, A., Lorén, N., von Corswant, C., Bolin, D., Rootzén, H., Olsson, E. 3D high spatial resolution visualisation and quantification of interconnectivity in polymer films

Barman, S., Rootzén, H., Bolin, D. New measures of bottleneck effects in pore geometries evaluated through prediction of diffusive transport

Material science is a cross-disciplinary field, including physics, chemistry and mechanical engineering. In this thesis porous materials are studied using tools from mathematical statistics and physics. One example of porous materials are pharmaceutical coatings that are used to control how fast drug is released from oral tablets. The coatings become porous when in contact with water, and the pore structure controls the drug release rate. Slowing down the release rate means that the drug concentration can be kept at a more stable level and lowers the risk of side effects from the medication.

We have developed methods which capture properties of the pore geometry that determine the drug release rate. The methods are based on a virtual experimental setup, where virtual materials were generated from statistical models of the coating and drug transport was computed in each generated material using a computer model. Virtual experiments have the advantage that it is easy to generate a large dataset in the computer, and large datasets are needed to create good models of how the pore geometry influences the drug transport. Real experiments are much more time-consuming and costly. We also developed statistical methods which were used to create realistic 3D statistical models of the coating structure. One of the main results from the virtual experiments was a set of new methods for capturing a type of bottleneck effect that can slow down the rate the drug is released.

Material structures seen through microscopes and statistics

Swedish Foundation for Strategic Research (SSF), 2014-04-01 -- 2019-06-30.

Subject Categories

Materials Engineering

Physical Chemistry

Probability Theory and Statistics

Areas of Advance

Materials Science



Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie: 4740


Chalmers University of Technology

Pascal, Matematiska vetenskaper, Chalmers tvärgata 3


Opponent: Prof. Rasmus Waagepetersen, Department of Mathematical sciences, Aalborg University, Denmark

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